Monochromatic light of wavelength 600 nm is incident from air onto a water surface. The wavelength and speed of light respectively in water will be
(Given: Refractive index of water = 4/3)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $450\, nm; 2.25 × 10^8\, m/s$
Given:
Wavelength in air, $\lambda_0 = 600 \ \text{nm}$
Refractive index of water, $n = 4/3$
Speed of light in air, $c = 3 \times 10^8 \ \text{m/s}$
Speed of light in water: $v = \frac{c}{n} = \frac{3 \times 10^8}{4/3} = 2.25 \times 10^8 \ \text{m/s}$
Wavelength in water: $\lambda = \frac{v}{f} = \frac{v}{c} \lambda_0 = \frac{2.25 \times 10^8}{3 \times 10^8} \cdot 600 \ \text{nm} = 450 \ \text{nm}$
Wavelength = 450 nm, Speed = 2.25 × 10⁸ m/s